Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2304.09094 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913788924526592 |
|---|---|
| author | Kofnov, Andrey Bartocci, Ezio Bura, Efstathia |
| author_facet | Kofnov, Andrey Bartocci, Ezio Bura, Efstathia |
| contents | We propose the K-series estimation approach for the recovery of unknown univariate and multivariate distributions given knowledge of a finite number of their moments. Our method is directly applicable to the probabilistic analysis of systems that can be represented as probabilistic loops; i.e., algorithms that express and implement non-deterministic processes ranging from robotics to macroeconomics and biology to software and cyber-physical systems. K-series statically approximates the joint and marginal distributions of a vector of continuous random variables updated in a probabilistic non-nested loop with nonlinear assignments given a finite number of moments of the unknown density. Moreover, K-series automatically derives the distribution of the systems' random variables symbolically as a function of the loop iteration. K-series density estimates are accurate, easy and fast to compute. We demonstrate the feasibility and performance of our approach on multiple benchmark examples from the literature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_09094 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Moment-based Density Elicitation with Applications in Probabilistic Loops Kofnov, Andrey Bartocci, Ezio Bura, Efstathia Methodology Numerical Analysis Symbolic Computation Systems and Control Applications 62G07, 60E05 (Primary) 60B10 (Secondary) G.3; I.1.1 We propose the K-series estimation approach for the recovery of unknown univariate and multivariate distributions given knowledge of a finite number of their moments. Our method is directly applicable to the probabilistic analysis of systems that can be represented as probabilistic loops; i.e., algorithms that express and implement non-deterministic processes ranging from robotics to macroeconomics and biology to software and cyber-physical systems. K-series statically approximates the joint and marginal distributions of a vector of continuous random variables updated in a probabilistic non-nested loop with nonlinear assignments given a finite number of moments of the unknown density. Moreover, K-series automatically derives the distribution of the systems' random variables symbolically as a function of the loop iteration. K-series density estimates are accurate, easy and fast to compute. We demonstrate the feasibility and performance of our approach on multiple benchmark examples from the literature. |
| title | Moment-based Density Elicitation with Applications in Probabilistic Loops |
| topic | Methodology Numerical Analysis Symbolic Computation Systems and Control Applications 62G07, 60E05 (Primary) 60B10 (Secondary) G.3; I.1.1 |
| url | https://arxiv.org/abs/2304.09094 |